Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Spintronics

Phonon-induced superconductivity in a self-consistent Hubbard model (Conference Presentation)

Enrique Muñoz, E. Vernek, V. M. Apel

Published Oct 11, 2017• 0 citations
Publisher

Abstract

We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model, formulated in terms of thermal Green's functions, shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.

DOI
10.1117/12.2276951

Related papers

Superconductivity and Hybridization in the Fermion System at Zero Temperature

P. Tarasewicz

Some ground state properties of a fermion system are investigated. An initial Hamiltonian being a generalization of the lattice Anderson model describes this system as a two-band electron-phonon one where both of electron bands are narrow (one is wider than the other). Two bands are hybridized and electrons from both of them are strongly coupled to the same local phonons. After performing the Lang–Firsov type transformation, a new polaron Hamiltonian is obtained. As a result, there appear three effective polaron-polaron interactions in this Hamiltonian and the bandwidths of both of electron bands are reduced. It is assumed that the reduction of the bandwidth of one of the bands is sufficiently strong to make this band dispersionless. Each of the interactions can lead to superconductivity on its own but only one of them is taken into account at this stage; it is the interaction between electrons from the band with a dispersion. The Bogolyubov’s mean field approach is used in order to find the spectrum of the reduced effective Hamiltonian. The effect of the hybridization on the superconducting gap and the relationship between the critical hybridization and the average number of electrons from the wider band per lattice site are investigated.

Journal of Superconductivity and Novel Magnetism•Oct 18, 2011•1 citation

Formation of bipolarons in the Holstein Hubbard model in one, two and three dimensions

Shreekantha Sil

In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.

Journal of Physics Condensed Matter•Oct 27, 1999•5 citations

Magnetism and Superconductivity in a Two-band Hubbard Model in Infinite Dimensions

Yoshiaki Ōno, Kazuhiro Sano

We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density $n=2$, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction $U$ is varied for a fixed value of the charge-transfer energy $Δ$. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping $|n-2|$, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of $n$. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near $n=1$ ($n=3$) where the system is Mott insulator which shows antiferromagnetism at low temperature.

arXiv:cond-mat/0304624•Journal of the Physical Society of Japan•Jan 1, 2002•1 citation

Thermodynamic Green functions in theory of superconductivity

Плакида

A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models.A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function.By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations.A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.

Condensed Matter Physics•Jan 1, 2006•8 citations

Strong interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model

V. A. Moskalenko, P. Entel, D. F. Digor

We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model. The Lang-Firsov canonical transformation allows us to obtain mobile polarons for which a diagram technique and generalized Wick's theorem is used. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud propagators. The pairing of electrons in the presence of acoustical phonon clouds is discussed and the critical temperature of the superconducting phase transition is determined for the special case $U<0$, where $U$ is the renormalized value of the on-site Coulomb repulsion. The renormalization is caused by the electron-phonon interaction.

Physical Review B•Aug 22, 2006•4 citations

Dynamic Hubbard model: Effect of finite boson frequency

F. Marsiglio, Robert Teshima, J. E. Hirsch

Dynamic Hubbard models describe coupling of a boson degree of freedom to the on-site electronic double occupancy. In the limit of infinite boson frequency this coupling gives rise to a correlated hopping term in the effective Hamiltonian and to superconductivity when the Fermi level is near the top of the band. Here we study the effect of finite boson frequency through a generalized Lang-Firsov transformation and a high-frequency expansion. It is found that finite frequency enhances the tendency to superconductivity in this model.

arXiv:cond-mat/0307594•Physical review. B, Condensed matter•Dec 11, 2003•14 citations
We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model, formulated in terms of thermal Green's functions, shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.
Some ground state properties of a fermion system are investigated. An initial Hamiltonian being a generalization of the lattice Anderson model describes this system as a two-band electron-phonon one where both of electron bands are narrow (one is wider than the other). Two bands are hybridized and electrons from both of them are strongly coupled to the same local phonons. After performing the Lang–Firsov type transformation, a new polaron Hamiltonian is obtained. As a result, there appear three effective polaron-polaron interactions in this Hamiltonian and the bandwidths of both of electron bands are reduced. It is assumed that the reduction of the bandwidth of one of the bands is sufficiently strong to make this band dispersionless. Each of the interactions can lead to superconductivity on its own but only one of them is taken into account at this stage; it is the interaction between electrons from the band with a dispersion. The Bogolyubov’s mean field approach is used in order to find the spectrum of the reduced effective Hamiltonian. The effect of the hybridization on the superconducting gap and the relationship between the critical hybridization and the average number of electrons from the wider band per lattice site are investigated.
In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.
We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density n=2n=2n=2, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction UUU is varied for a fixed value of the charge-transfer energy ΔΔΔ. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping ∣n−2∣|n-2|∣n−2∣, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of nnn. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near n=1n=1n=1 (n=3n=3n=3) where the system is Mott insulator which shows antiferromagnetism at low temperature.
A general theory of superconductivity is formulated within the thermodynamic Green function method for various types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models.A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function.By applying the noncrossing approximation for the self-energy, a closed selfconsistent system of equations is obtained, similar to the conventional Eliashberg equations.A brief discussion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given.
We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model. The Lang-Firsov canonical transformation allows us to obtain mobile polarons for which a diagram technique and generalized Wick's theorem is used. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud propagators. The pairing of electrons in the presence of acoustical phonon clouds is discussed and the critical temperature of the superconducting phase transition is determined for the special case U<0U<0U<0, where UUU is the renormalized value of the on-site Coulomb repulsion. The renormalization is caused by the electron-phonon interaction.
Dynamic Hubbard models describe coupling of a boson degree of freedom to the on-site electronic double occupancy. In the limit of infinite boson frequency this coupling gives rise to a correlated hopping term in the effective Hamiltonian and to superconductivity when the Fermi level is near the top of the band. Here we study the effect of finite boson frequency through a generalized Lang-Firsov transformation and a high-frequency expansion. It is found that finite frequency enhances the tendency to superconductivity in this model.